arXiv:2603.29833v1 Announce Type: new Abstract: In many systems, communication proceeds by broadcasting rather than single source-target routing, but network structures that maximize signal lifetime are not well understood. Degree correlations are known to influence robustness and spreading, yet their effect on signal persistence has remained unclear. Here we introduce Copy-Spread-Annihilate dynamics, a minimal synchronous broadcasting model with annihilation. We show that signal lifetimes vary non-monotonically with assortativity and are maximized near neutral assortativity, where hub-driven amplification is strong but annihilation via short cycles is still limited. Applying this framework to the mouse connectome suggests assortativity as a structural control parameter for broadcast signal persistence in brain-like and other complex networks.

arXiv:2603.12878v1 Announce Type: new Abstract: The synchronized activity of neuronal populations can lead to pathological over-synchronization in conditions such as epilepsy and Parkinson disease. Such states can be desynchronized by brief electrical pulses. But when the underlying oscillating system is not known, as in most practical applications, to determine the specific times and intensities of pulses used for desynchronizaton is a difficult inverse problem. Here we propose a desynchronization scheme for neuronal models of bi-variate neural activity, with possible applications in the medical setting. Our main argument is the existence of a peculiar point in the phase space of the system, the centroid, that is both easy to calculate and robust under changes in the coupling constant. This important target point can be used in a control procedure because it lies in the region of minimal return times of the system.

arXiv:2603.03870v1 Announce Type: new Abstract: We introduce a two-phase quadratic integrate-and-fire (QIF) neuron whose membrane potential evolves according to two alternating Riccati equations within finite bounds. This simple extension removes the unphysical voltage divergence of the standard QIF model while producing realistic spike waveforms. Despite this modification, the system retains an exact low-dimensional description in the thermodynamic limit, governed by a single complex Riccati equation. Expressions for collective quantities such as the firing rate and mean voltage remain compact and analytically tractable. Because the formalism preserves the mathematical structure of the standard QIF ensemble, it inherits its many generalizations and can serve as a drop-in replacement in existing mean-field frameworks, providing a more biologically plausible yet still exactly solvable neuronal model.